Who was Pythagoras?

We recognize the name “Pythagoras” because it is attached to a theorem, one that most of us have grappled with at school. The square on the Pythagoras of a right angled triangle is equal to the sum of squares on the other two sides. That is, if you take any right-angled triangle, then the square of the longest side is equal to the sum of the squares of the other two sides. Well known as his theorem may be, the actual person has proved rather elusive, although we know more about him as a historical figure, than we do for, say, Euclid. What we don’t know is whether he proved his eponymous theorem, and there are good reasons to suppose that even if he did, he wasn’t the first one to do so.

But more of that story later.

Pythagoras was Greek, born around 569BC on the island of Samos in the north-eastern Aegean. (The exact date is disputed, but this one is wrong by at most 20 years.) His father, Mnesarchus was a merchant from Tyre; his mother, Pythais, was from Samos. They may have met when Mnesarchus brought corn to Samos during a famine, and was publicly thanked by being made a citizen.

Pythagoras studied philosophy under Pherekydes. He probably visited another philosopher, Thales of Miletus. He attended lectures given by Anaximander, a pupil of Thales, and absorbed many of his ideas on cosmology and geometry. He visited Egypt, was captured by Cambyses, II, the King of Persia, and taken to Babylon as a prisoner. There he learned Babylonian mathematics and musical theory. Later he found the school of Pythagoreans in the Italian city of Croton (now, Crotone), and it is for this that he is best remembered. The Pythagoreans were a mystical cult. They believed that the universe is mathematical, and that various symbols and numbers have a deep spiritual meaning.

Various ancient writers attributed various mathematical theorems to the Pythgoreans, and by extension to Pythagoras — notably, his famous theorem about right-angled triangles. But we have no idea what mathematics Pythagoras himself originated. We don’t know whether Pythagoreans could prove his theorem, or just believed it to be true. And there is evidence from the inscribed clay tablet known as Plimpton 322 that the ancient Babylonians may have understood the theorem 1200 years earlier — though they probably didn’t possess a proof, because Babylonians didn’t go much for proofs anyway.